Problem: Simplify the following expression: $q = \dfrac{2}{5x} + \dfrac{9}{4x}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5x$ and $4x$ $\lcm(5x, 4x) = 20x$ $ q = \dfrac{4}{4} \cdot \dfrac{2}{5x} + \dfrac{5}{5} \cdot \dfrac{9}{4x} $ $q = \dfrac{8}{20x} + \dfrac{45}{20x}$ $q = \dfrac{8 +45}{20x}$ $q = \dfrac{53}{20x}$